This invention relates to a filter circuit and, in particular, to a band pass filter having a linear phase shift, short group delay, and separately controllable roll-off and ripple.
Band pass filters have been used, alone or combined, in a host of applications virtually since the beginning of the electronic industry. The continuing problem in any application is providing a band pass filter having the desired frequency response. It is known in the art that a band pass filter can include a pair of series coupled resonant circuits that are xe2x80x9cde-tunedxe2x80x9d, i.e. have slightly different resonant frequencies. See for example, xe2x80x9cRadio Engineeringxe2x80x9d by Terman, McGraw-Hill Book Company, New York, 1937, pages 76-85.
Today, a band pass filter can be implemented in any one of several technologies. For example, passive analog filters utilize resistors, capacitors, and inductors to achieve the desired frequency response. Active filters add one or more operational amplifiers to prevent a signal from becoming too attenuated by the passive components and to exaggerate or to minimize a particular response by controlled feedback. Switched capacitor circuits are basically analog circuits but divide a signal into discrete samples and, therefore, have some attributes of digital circuits.
Finite Impulse Response (FIR) filters are completely digital, using a shift register with a plurality of taps. An FIR filter generally has a linear phase versus frequency response and a constant group delay. As such, FIR filters find widespread use in digital communication systems, speech processing, image processing, spectral analysis, and other areas where non-linear phase response is unacceptable.
A problem using FIR filters is the number of samples versus the delay in processing a signal. In order to obtain a high roll-off, i.e. a nearly vertical skirt on the response curve, a very large number of taps is necessary. Although the group delay is constant, it is relatively large, ten to fifteen times that of an analog filter, because of the large number of taps. Another problem with FIR filters is ripple, which typically exceeds 3 decibels (dB). There are other digital circuits that could be considered filters but these circuits either do not operate in xe2x80x9creal timexe2x80x9d or have such long processing times that the delays limit the utility of the techniques.
A problem with a band pass filter is phase distortion, which is proportional to the Q of the filter. A band pass filter has a phase shift associated with it and the phase shift tends to change the most quickly, i.e. non-linearly, at the center frequency of the filter. Signals passing through several band pass filters can acquire a considerable amount of distortion when, in fact, one is trying to improve fidelity. This is particularly true in telephone systems where a signal may be filtered several times on its way from a first telephone, across a switching network, and through a second telephone.
Obtaining a sharp roll-off from an analog filter is often difficult, particularly for narrow band filters, e.g. one third octave or less. Even with active elements, good filters tend to be complex and, therefore, expensive. As noted above, FIR filters can provide a sharp roll-off but typically suffer from longer group delay, making an FIR filter unsuitable in telephone systems, for example.
Frequency response, phase shift linearity, group delay, ripple, and roll-off are characteristics of all filters, whether or not the characteristic is mentioned in a particular application. The Q, or sharpness, of a filter circuit is often specified as the ratio of the center frequency to the band width at xe2x88x923 dB. A problem with this definition is that the roll-off on each side of the center frequency is assumed to be symmetrical (when amplitude is plotted against the logarithm of frequency). A similar but less critical assumption is made when specifying the band width of a filter as the separation of the xe2x88x9220 dB points in a response curve. If the assumption is not valid, then comparing one filter to another becomes difficult.
In view of the foregoing, it is therefore an object of the invention to provide a band pass filter with a nearly linear phase shift.
Another object of the invention is to provide a band pass filter with short, relatively constant, group delay
A further object of the invention is to provide a band pass filter with reduced phase distortion.
Another object of the invention is to provide a band pass filter that is relatively inexpensive despite improved performance when compared with filters of the prior art.
A further object of the invention is to provide a band pass filter having an adjustable ripple;
Another object of the invention is to provide a band pass filter that has an easily adjustable Q.
A further object of the invention is to provide a band pass filter with individually adjustable roll-off on either side of center frequency.
Another object of the invention is to provide a band pass filter having separately adjustable Q and ripple.
The foregoing objects are achieved in this invention in which an electrical signal is applied to a pair of notch filters having different center frequencies and the output of one notch filter is subtracted from the output of the other notch filter. A band pass filter can also be made from the difference in outputs of a pair of band pass filters. The filters preferably have response curves that intersect at xe2x88x923 dB. The separation of the center frequencies determines, in part, the ripple in the response curve of the combined band pass filter. The invention can be implemented with active filters, IIR (Infinite Impulse Response) filters, bi-quad filters, or switched-C filters.